Octant-Based Stencil Selection for Meshless Finite Difference Methods in 3D
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We study a simple meshless stencil selection algorithm in 3D for supporting the meshless finite difference method based on radial basis functions (RBF-FD) to solve the Dirichlet problem for the Poisson equation. Our numerical experiments show that the proposed method produces solutions that differ very little from the solutions by the finite element method with Courant’s piecewise linear basis functions, when the domain is discretized by the vertices of the respective tetrahedral triangulation.
KeywordsRBF-FD Meshless methods Generalized finite differences
Mathematics Subject Classification (2010)65M06 65N06
This paper was supported by Thai Nguyen University under grant number DH2015-TN07-03. We are grateful to three anonymous referees for their useful suggestions that have helped to improve our paper.
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